I have always seen the formulas of rotation having cross product of $\vec{r}$ and some linear quantity. For e.g. $\vec{\tau} = \vec{r}$ x $\vec{F}$, $\vec{L} = \vec{r}$ x $\vec{p}$ etc. But we have never been told the source of these formulas. I never understood where they came from and what is their derivation. Is the direction of rotational quantities just a reference and accordingly, in consideration with magnitudes we have derived a cross product?
I have been pondering upon this question for half a year but I had no success.
